Solve the Inequality for x y<=5/3x-4

$y \leq \frac{5}{3} x - 4$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$\frac{5}{3} x - 4 \geq y$

Step 2

Combine $\frac{5}{3}$ and $x$ .

$\frac{5 x}{3} - 4 \geq y$

Step 3

Add $4$ to both sides of the inequality.

$\frac{5 x}{3} \geq y + 4$

Step 4

Multiply both sides by $3$ .

$\frac{5 x}{3} \cdot 3 \geq (y + 4) \cdot 3$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 x}{3} \cdot 3 \geq (y + 4) \cdot 3$

Rewrite the expression.

$5 x \geq (y + 4) \cdot 3$

Simplify the right side.

Simplify $(y + 4) \cdot 3$ .

Apply the distributive property.

$5 x \geq y \cdot 3 + 4 \cdot 3$

Simplify the expression.

Move $3$ to the left of $y$ .

$5 x \geq 3 \cdot y + 4 \cdot 3$

Multiply $4$ by $3$ .

$5 x \geq 3 y + 12$

Step 6

Divide each term in $5 x \geq 3 y + 12$ by $5$ and simplify.

Divide each term in $5 x \geq 3 y + 12$ by $5$ .

$\frac{5 x}{5} \geq \frac{3 y}{5} + \frac{12}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{3 y}{5} + \frac{12}{5}$

Divide $x$ by $1$ .

$x \geq \frac{3 y}{5} + \frac{12}{5}$